Mathematics and Statistics Vol. 8(3), pp. 262 - 277
DOI: 10.13189/ms.2020.080304
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MTSD-TCC: A Robust Alternative to Tukey's Control Chart (TCC) Based on the Modified Trimmed Standard Deviation (MTSD)

Moustafa Omar Ahmed Abu-Shawiesh ^1,*, Muhammad Riaz ², Qurat-Ul-Ain Khaliq ^3
1 Department of Mathematics, Faculty of Science, The Hashemite University, Jordan
² Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
³ Department of Higher Education, Government Degree College Jhelum, Pakistan

ABSTRACT

In this study, a robust control chart as an alternative to the Tukey's control chart (TCC) based on the modified trimmed standard deviation (MTSD), namely MTSD-TCC, is proposed. The performance of the proposed and the competing Tukey's control chart (TCC) is measured using different length properties such as average run length (ARL), standard deviation of run length (SDRL), and median run length (MDRL). Also, the study covered normal and contaminated cases. We have observed that the proposed robust control chart (MTSD-TCC) is quite efficient at detecting process shifts. Also, it is evident from the simulation results that the proposed robust control chart (MTSD-TCC) offers superior detection ability for different trimming levels as compared to the Tukey's control chart (TCC) under the contaminated process setups. As a result, it is recommended to use the proposed robust control chart (MTSD-TCC) for process monitoring. An application numerical example using real-life data is provided to illustrate the implementation of the proposed robust control chart (MTSD-TCC) which also supported the results of the simulation study to some extent.

KEYWORDS
Tukey's Control Chart (TCC), Average Run Length (ARL), Inter-Quartile Range (IQR), Robust Estimator, Statistical Process Control (SPC), Modified Trimmed Standard Deviation (MTSD), Outliers

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Moustafa Omar Ahmed Abu-Shawiesh , Muhammad Riaz , Qurat-Ul-Ain Khaliq , "MTSD-TCC: A Robust Alternative to Tukey's Control Chart (TCC) Based on the Modified Trimmed Standard Deviation (MTSD)," Mathematics and Statistics, Vol. 8, No. 3, pp. 262 - 277, 2020. DOI: 10.13189/ms.2020.080304.

(b). APA Format:
Moustafa Omar Ahmed Abu-Shawiesh , Muhammad Riaz , Qurat-Ul-Ain Khaliq (2020). MTSD-TCC: A Robust Alternative to Tukey's Control Chart (TCC) Based on the Modified Trimmed Standard Deviation (MTSD). Mathematics and Statistics, 8(3), 262 - 277. DOI: 10.13189/ms.2020.080304.